1. Field of the Invention
The invention relates generally to methods and apparatus for nuclear magnetic resonance (NMR) spectroscopy.
2. Background Art
Electromagnetic based instruments for measuring properties of matter or identifying its composition are well known. The nuclear magnetic resonance (NMR) technique has been used to form images of biological tissues or to determine the composition of, for example, earth formations.
Apparatus for nuclear magnetic resonance measurements are well known in the art. Generally, apparatus for nuclear magnetic resonance measurements include magnets to form a static magnetic field and antennas for transmitting and receiving radio frequency magnetic fields. The antennas usually are solenoid coils located close to the region to be analyzed. Example of NMR are disclosed in U.S. Pat. No. 4,350,955 issued to Jackson et al. and U.S. Pat. No. 4,717,877 issued to Taicher et al.
The nuclear magnetic resonance phenomenon is exhibited by atomic nuclei with an odd total number of protons and neutrons. When placed in an externally applied static magnetic field, Bo, the atomic nuclei tend to align themselves with the applied field and produce a net magnetization, M, in the direction of the applied field. The nuclei precess about the axis of the applied field with a characteristic NMR frequency ω (called the Larmor frequency) given by the equation:ω=γBo  (1) where γ is the gyromagnetic ratio.
A time-dependent (RF) magnetic field, having frequency components equal to the atomic nuclei's specific Larmor frequency, and that is applied in a direction orthogonal to the static magnetic field Bo, will make the nuclei absorb energy and nutate away from the axis of the static magnetic field Bo. If the RF pulse is turned off precisely when the angle of nutation reaches 90°, the magnetization falls into a plane transverse to the direction of Bo (the x-y plane) and the net magnetization now precesses about the static magnetic field Bo in the transverse plane at the Larmor frequency. Such a pulse is called a 90° pulse. A 180° pulse is one which nutates the magnetization through 180°, inverting it. These two types of RF pulse form the basic tools of NMR spectroscopy.
FIGS. 2a and 2b show pulse sequences typically used in NMR spectroscopy. FIG. 2a shows the above described 90° pulse on the upper graph, and a detected signal on the lower graph. FIG. 2b shows the spin-echo pulse sequence. A 90° pulse is first applied to the atomic nuclei system. The 90° degree pulse rotates the corresponding magnetization into the x-y plane. The transverse magnetization begins to dephase. At some point in time after the 90° pulse, a 180° pulse is applied. This pulse rotates the magnetization by 180° about the x axis. The 180° pulse causes the magnetization to at least partially rephase forming a signal called an echo. Therefore, the 180° is referred to as refocusing pulse. The lower graph in FIG. 2b shows the detected signal.
Not only 90° pulses are used. Repeating several small flip angles (<90°) RF pulses are also useful in order to produce high signal to noise ratios (S/N). The advantage of using small flip angle RF pulse is that after the RF pulse there are still remains of magnetization along the z axis. The remaining magnetization can be used for the observation of the next NMR signal. Therefore, one can repeat the application of another small flip angle RF pulse without having to wait for the return of magnetization along the z axis. The time constant with which the magnetization returns to the Z axis after the RF pulse is called the spin-lattice relaxation time (T1). The application of small flip angle RF pulse permits the repetition of subsequent RF pulses without the magnetization vector having reached its equilibrium value. For a fixed time, it is possible to acquire a series of NMR signals with small flip angle and small repetition times instead of a single 90° RF pulse. Therefore, the signal to noise ratio (S/N) is greater using a series of small flip angles than when using a single 90° RF pulse.
The optimum small flip angle α and the small flip angles pulse spacing τ are related to the relaxation time T1 by the relationship:cos α=exp(−τ/T1). 
It is known that the observed NMR signal strength depends on the flip angle, repetition time, and T1. The initial amplitude of the FID signal is given by:M=Mo[(1−E1)/(1−E1 cos β)] sin βwhere
E1=exp(−T/T1)
T1=spin-lattice relaxation time
T=repetition time
β=flip angle
FIG. 9 shows a plot of the normalized peak FID amplitude as a function of flip angle (β) for various values of T/T1.
For example, the signal amplitude is 50% of full amplitude with 50° flip angle when the repetition time is 50% of T1. The FID signal amplitude for maximum signal is with 90° flip angle with the re[etition time of 5T1. Within a time of 5T1, the 50° flip angle can be repeated 10 times and the increase in S/N is 58%.
Experimentally, the NMR signal is detected by a tuned RF coil with its axis perpendicular to the static magnetic field Bo. The same coil used for excitation is also suitable for detection, or alternatively, a separate, mutually orthogonal coil can be used. The oscillating NMR magnetization induces a voltage in the coil. These NMR signals may be detected and Fourier-transformed to derive the frequency components of the NMR signals characteristic of the excited nuclei.
The decay in the signal amplitude over time is due to spin-spin relaxation phenomena and the fact that each atomic nucleus experiences a slightly different magnetic field. At the signal's maximum value all atomic nuclei precess in unison. As time elapses, the greater will be the phase differences between atomic nuclei and the total contribution of the magnetization vectors of each atomic nucleus will inevitably sum to zero.
The atomic nuclei experience different magnetic field values with respect to each other generally due to inhomogeneities in the static magnetic field Bo, the chemical shift phenomenon, or due to internal (sample-induced) magnetic field inhomogeneity.
The static magnetic field Bo inhomogeneities can be due to imperfections in the corresponding magnetic field source. Also, the strength of the static magnetic field Bo experiences a fall-off the further it is measured from the static magnetic field source, as shown in FIG. 3. This is called the gradient of the magnetic field. The gradient has a slope defined by the amount of change of the magnetic field strength divided by the displacement from the magnetic field source. A gradient such that the magnetic field strength decreases the further it is measured from the magnetic field source is defined as having a negative slope (dB/dx<0). Magnetic fields whose strength increases the further it is measured from the magnetic field source are defined as having gradients with positive slopes (dB/dx>0).
The chemical shift phenomenon occurs when an atom is placed in a magnetic field. The electrons of the atom circulate about the direction of the applied magnetic field causing a magnetic field at the nucleus which will contribute to the total value of the magnetic field applied to the nucleus of the atom.
Examples of internal (sample-induced) magnetic field inhomogeneities are interfaces between media having different magnetic susceptibilities, such as grain-pore fluid interface in earth formations.
The measurable signal (Free induction decay, FID) lasts only as long as the atomic nuclei precess in unison. The time period in which the signal decays to zero is referred to as free induction decay time.
It has been noted that the signal decays exponentially with respect to time, therefore:M(t)=Moe(−t/T2*)  (1) where Mo is the modulus of the initial magnetization vector and T2* is called the time decay constant and it is the time required to reduce Mo by a factor of e. The inverse of T2* (1/T2*) is the rate at which Mo's value reduces in a specific time period t.
As previously described, the decay of the signal amplitude can be due to the inhomogeneities of the net magnetic field applied on the excited region. These inhomogeneities can be product of the gradient of the static magnetic field, chemical shift and sample induced inhomogeneities. Each of the above mentioned phenomena will contribute its own specific rate to reduce the net magnetization vector. Therefore,1/T2*=1/T2+1/T2′+γΔBo 
Where, for example, 1/T2 is due to spin-spin relaxation, 1/T2′ is the sample induced inhomogeneities' rate and γΔBo corresponds to the static field inhomogeneity contribution. Equation 1 can be rewritten as:M(t)=Mo[e−t(T2+T2′+tγΔBo)]  (2) 
Therefore, the (FID) decay time following the 90° RF pulse can result from the magnetic field inhomogeneity of the static field Bo, spin-spin relaxation time (T2) and the sample induced inhomogeneities' time (T2′) as shown in equation 2.
The NMR signal will be emitted from a region located in the sample being irradiated by the RF signal. This region is called the excited region. FIG. 3 shows exited region (12) having a thickness Δx. It is known that the stronger the RF signal is, the greater will be the value of Δx. A greater Δx will imply a greater drop in the static magnetic field's value across the excited region which implies a greater inhomogeneity in the static magnetic field (ΔBo) and an inevitable faster decay of the signal as can be seen in equation 2. Therefore, as the strength of the RF field is increased, the duration of the signal will decrease substantially.
However, thicker (greater Δx) excited regions will result, for example, in higher detectable signals, such as CPMG sequence (Carll-Purcell-Meiboom-Gill) echo signals. The CPMG sequence consists of a 90° pulse followed by a number of 180° pulses between which echoes occur.
Therefore, it is desirable to be able to modify or even cancel out, while undertaking NMR measurements, a specific contribution for the FID decay time, such as, for example, the magnetic field inhomogeneity of the static magnetic field Bo.
Moreover, it is desirable to also modify the gradient of the net static magnetic field applied to the excited region in order to induce echo signals once the original gradient of the applied static magnetic field Bo is restored.